Confusion over animations in the Dope Sheet and NLA Editor
The action that will be played will be the priority one on the NLA, i.e. the one on top track, except:


1: If you've selected a strip in the NLA and pressed tab to edit its action in the Dopesheet/Action Editor. To come back to the normal NLA running, press tab again on the NLA (or press the X button on the right of the action name in the Dopesheet/Action Editor).
2: If you've loaded an animation in the Dopesheet/Action Editor mode from the dropdown menu. To come back to the normal NLA running, press the X button on the right of the action name.


But be careful: If the animation you've selected misses keyframes for some of its bones, these bones may be playing some inexplicable keyframes, actually coming from other NLA strips below your one or from previous animation. To prevent this to happen you can press the star icon of your track or mute the others. But the best thing to do is to keyframe your whole armature in Pose mode, at the beginning of each action, to make sure that no bone will inherit pose from another action, unless you have a good reason not to.

Also, about NLA strips: If you want the keyframes of an animation strip to continue to influence the armature even after the end of the strip length, choose the Hold option in the Extrapolation dropdown menu of the Properties panel of the NLA (activate with N > Animations > Active Strip.

About actions: Don't forget to press the F button on the right of the action name, in the Dopesheet/Action Editor mode. This way you're sure this action won't be deleted when you'll reopen your file, even if it's not used anywhere.

About your foot hobbling, it happens in the middle of your action, frame 20 when the left foot is forward. To fix it, go in Pose mode, select all the bones at frame 0 (or at least the leg bones), ctrlC, come to frame 20, where the pose is supposed to be inverted, select all your bones and press shiftctrlV, then i to keyframe the pose. It works.